Problem: $K$ is the midpoint of $\overline{JL}$ J K L If: $ JK = 8x + 7$ and $ KL = 4x + 43$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x + 7} = {4x + 43}$ Solve for $x$ $ 4x = 36$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({9}) + 7$ $ KL = 4({9}) + 43$ $ JK = 72 + 7$ $ KL = 36 + 43$ $ JK = 79$ $ KL = 79$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {79} + {79}$ $ JL = 158$